According to a hadith narrated by Abu Hurairah (RA):
The Prophet (SAW) said, "Avoid the seven great destructive sins."
The people enquired, "O Allah's Apostle! What are they?
"He said,
To join others in worship along with Allah (SWT),
To practice sorcery,
To kill the life which Allah has forbidden except for a just cause,
(according to Islamic law),
To eat up Riba (usury),
To eat up an orphan's wealth,
To give back to the enemy and fleeing from the battlefield at the
time of fighting,
And to accuse, chaste women, who never even think of anything
touching chastity and are good believers."
(Sahih Bukhari, Volume 4, Book 51, Number 28; Volume 8, Book 82,
Number 840)
Although the sins mentioned in the above Hadith are "the seven
great destructive sins", one should abstain from all sins mentioned
in the Quran and in Hadiths where there is a mention of the Curse
of Allah (SWT) and of the angels or the wrath and anger of Allah
(SWT) or punishment in Hell-Fire. One should also abstain from
those sins which are punishable in this world for example murder,
stealing, spreading mischief in the land by waging war against
Allah (SWT) and His Messenger, fornication, adultery,
homosexuality, drinking alcohol, falsely accusing chaste women of
fornication or adultery and not producing four witnesses etc.
The greatest of all of the major sins is to join others in worship
along with Allah (SWT), when none has the right to be worshipped
except Him and to die as a disbeliever.
Allah (SWT) says in Surah Al-Baqarah, (Verses 161 & 162),
Verily, those who disbelieve, and die while they are disbelievers,
it is they on whom is the Curse of Allah and of the angels and of
mankind, combined.
They will abide therein (under the curse in Hell), their punishment
will neither be lightened, nor will they be reprieved.
and in Surah Al-Baqarah, (Verse 165):
And of mankind are some who take (for worship) others besides Allah
as rivals (to Allah). They love them as they love Allah. But those
who believe, love Allah more (than anything else). If only, those
who do wrong could see, when they will see the torment, that all
power belongs to Allah and that Allah is Severe in punishment.
Allah (SWT)also says in Surah Al-Baqarah, (Verses 166 & 167),
When those who were followed, disown (declare themselves innocent
of) those who followed (them), and they see the torment, then all
their relations will be cut off from them.
And those who followed will say: "If only we had one more chance to
return (to the worldly life), we would disown (declare ourselves as
innocent from) them as they have disowned (declared themselves as
innocent from) us." Thus Allah will show them their deeds as
regrets for them. And they will never get out of the Fire.
Verily, those who disbelieved, and died while they were
disbelievers, the (whole) earth full of gold will not be accepted
from anyone of them even if they offered it as a ransom. For them
is a painful torment and they will have no helpers.
(Surah Âl-'Imrân Verse 91)

Narrated Anas bin Malik (RA):
Allah's Prophet used to say, "A disbeliever will be brought on the
Day of Resurrection and will be asked. "Suppose you had as much
gold as to fill the earth, would you offer it to ransom yourself?"
He will reply, "Yes." Then it will be said to him, "You were asked
for something easier than that (to join none in worship with Allah
i.e. to accept Islam, but you refused)."
(Sahih Bukhari Volume 8, Book 76, Number 546)
Narrated Anas (RA):

The Prophet said, "Allah will say to that person of the (Hell) Fire
who will receive the least punishment, 'If you had everything on
the earth, would you give it as a ransom to free yourself (i.e.
save yourself from this Fire)?' He will say, 'Yes.' Then Allah will
say, 'While you were in the backbone of Adam, I asked you much less
than this, i.e. not to worship others besides Me, but you insisted
on worshipping others besides me.' "
(Sahih Bukhari Volume 4, Book 55, Number 551)
It is narrated on the authority of Abu Huraira (RA) that the
Messenger (SAW) said to his uncle Abu Talib at the time of his
death:
"Make a profession of it, that there is no God but Allah and I will
bear testimony (of your being a Muslim) on the Day of Judgement".
But he (Abu Talib) refused to do so.
(Sahih Muslim Volume 1 Hadith No 37).
Then Allah (SWT) revealed this verse in Surah Al-Qasas, (Verse 56),
Verily! You (O Muhammad SAW) guide not whom you like, but Allah
guides whom He wills. And He knows best those who are the guided.
And in Surah At-Taubah, (Verse 113),
It is not (proper) for the Prophet and those who believe to ask
Allah's Forgiveness for the Mushrikûn (polytheists, idolaters,
pagans, disbelievers in the Oneness of Allah) even though they be
of kin, after it has become clear to them that they are the
dwellers of the Fire (because they died in a state of disbelief).